Fracture Energy In Mode Research Articles

Assessing critical fracture energy in mode I for bonded composite joints: A numerical–experimental approach with uncertainty analysis

The manufacturing process of composite structural components involves the assembly of composite parts using adhesives, which introduces variations in the geometrical and mechanical properties of bonded joints. The fracture energy under mode-I loading ( G I c) is a parameter used to predict crack propagation and evaluate the residual strength of the joint. This work proposes a numerical-experimental procedure to determine G I c in mode I, while considering the uncertainties inherent in the manufacturing process of bonded joints. The proposed procedure employs a three-dimensional finite element model to simulate a double cantilever beam test, using finite element commercial software. The cohesive zone model is applied to simulate the mechanical behavior of the adhesive, and experimental data are used to feed the computational model. A Plackett-Burman design is performed to reduce the number of experiments and evaluate the effect of the main influence parameters. Force-displacement curves are obtained, the compliance-based beam method is applied to determine G I c in mode I, employing both trapezoidal and triangular traction-separation laws. The results are thoroughly examined, taking into account the potential strengths and limitations of the proposed procedure, particularly in its application to predicting the behavior of bonded composite joints under mode I loading conditions. The proposed approach can help to understand the uncertainties effect related to the manufacturing process of bonded joints on G I c values, and improve the reliability of predicting crack propagation and residual strength assessment in bonded joints.

Influence of high temperatures on modes I and II fracture toughness and energy of nanoclay-reinforced polymer concrete

This paper investigates the influence of exposure to elevated temperatures on the fracture mechanics of polymer concrete (PC). The PC was synthesised using epoxy, silica sand, crushed basalt, and nanoclay. The prepared PC was exposed to temperatures of 24, 40, 60, 80, 100, 120 and 140°C for two hours, and the residual fracture toughness and fracture energy in mode I and mode II were studied. The three-point bending test was conducted on cracked semi-circular bend specimens with a crack angle of 0° (pure mode I) and 41° (pure mode II) to determine the fracture parameters. Subjection to high temperatures significantly increased the fracture toughness and fracture energy of the PC. The maximum fracture toughness and fracture energy were obtained after exposure to temperatures of 120°C and 140°C, respectively. Scanning electron microscopy was used to investigate the fracture surface of the PC. The type of fracture (brittle or ductile) of the PC before and after exposure to the target temperatures was evaluated. The mathematical relationships between modes I and II critical stress intensity factor (KIc and KIIc), as well as modes I and II fracture energy (GIf and GIIf) after exposure to high temperatures, were also determined.

Fracture energy and mechanical properties of toughened epoxy resin with eggshell powder

Eggshells are daily food waste disposed of in landfills, producing environmental issues and an unpleasant odour. Eggshells powder may be suitably applied as a filler in epoxy resins to improve their mechanical properties. The material properties and fracture energy of toughened epoxy with eggshell powder (TEEP) were measured and investigated. Dog-bone specimens were fabricated to investigate the mechanical properties of TEEP (i.e. elastic modulus, Poisson’s ratios and tensile strength) and tested under quasi-static tensile loading. Double Cantilever Beam (DCB) and End-Notched Flexure (ENF) tests were used to determine the mode I and Mode II fracture energies of TEEP specimens, respectively. For this purpose, oven-dried eggshells were crushed into particles size of 100 µm. The volume fraction of eggshell powder as filler in TEEP is designated as 0%, 2.5%, 5%, and 10%. The epoxy resin system was made by mixing EPIKOTE Resin 828 and Hardener 651 with a mixing ratio of 5:2 by weight. The results showed that the tensile strength, elastic modulus, fracture energy in Mode I and Mode II were optimum at TEEP 5% with an enhancement of 36.8%, 24.9%, 60.3% and 166.3%, respectively compared to that of neat epoxy. This is due to better surface roughness and the ability of eggshell powder as a crack arrestor. However, TEEP with 10% eggshell prone to agglomeration of eggshell powder caused poor bonding with epoxy resin and affect the mechanical properties.

Parametric investigation of bonded composite joints under Mode II using a new methodology based on design of experiments

ABSTRACT In the pursuit of a sustainable future with limited resources and growing environmental concerns, adhesive joining stands out as a pivotal technology for the advancement of lightweight structures. This study aims to investigate the influence of various variables on the critical strain energy release rate in mode II (GIIc) for End-Notched Flexure (ENF) bonded composite joints, employing a new methodology based on Design of Experiments (DoE) approach. Two-dimensional finite element models of the ENF bonded composite joints are developed using commercial software, with all numerical models generated via Python™ scripts linked with AbaqusⓇ. Eleven design parameters related to the specimen geometry and material properties are systematically evaluated to determine the influence of each variable on GIIc. Numerical force–displacement curves are obtained, followed by the application of the Compliance-Based Beam Method (CBBM) to estimate the critical fracture energy in mode II, represented by a numerical envelope. The influence of each parameter is assessed using the main effect (ME) metric. The top five most influential variables affecting GIIc and CBBM are identified as the adhesive’s critical strain energy release rate in mode II (GIIc), effective laminate longitudinal elastic modulus (), adhesive thickness (tA), adherent thickness (h), and pre-crack length (). Furthermore, the study highlights the epistemic uncertainty associated with the geometric variables. Despite the limitations inherent in the computational model, the Plackett-Burman method consistently proves effective in conducting sensitivity analysis of the variables in the ENF test. These findings demonstrate promising prospects for the application of this procedure in the design of composite joint structures.

Effect of notch depth ratio on mode I and mixed mode I-II fracture properties of engineered cementitious composites (ECC)

The effect of initial notch depth ratios (a/h) on the mode I and mixed mode I-II fracture properties of ECC was studied by using three-point bending test and four-point shear test, respectively. For mode I fracture, the initial fracture toughness KICini and unstable fracture toughness KICun- and KICun+ instead of KICun based on double-K fracture criterion are calculated. The mode I fracture energy GI is calculated by load-crack mouth opening displacement curve (P-CMOD). For mixed mode I-II fracture, the initial effective stress intensity factor (Keffini) are calculated by using nonlinear finite element software and the mixed mode fracture energy GI–II is analyzed. Also, crack propagation mechanism of ECC under mixed mode I-II fracture is analyzed from P-CMOD curve and load-crack mouth sliding displacement (P-CMSD) curve, and mixed mode I-II crack propagation of ECC is divided into six stage. It is found that when 0.3 ≤ a/h ≤ 0.8, the KICini does not change. While, KICun increases when a/h increases from 0.1 to 0.3, decreases when a/h increases from 0.3 to 0.7 and GI decreases with the a/h increasing from 0.3 to 0.8. GI–II is much larger than GI due to an obvious inclined fracture process zone with many micro-cracks dissipating energy in the mixed mode I-II fracture. The GI–II increases with the a/h increasing from 0.1 to 0.6 and decreases with the increase of the a/h from 0.6 to 0.8. While, the crack initiation angle increases with the increase of a/h in the mode I-II fracture.

Experimental comparison of two testing setups for characterizing the shear mechanical properties of masonry

The prediction of the structural capacity of masonry buildings against lateral loads requires an accurate characterization of the masonry strength and the general response under shear stresses. The experimental determination of shear strength parameters typically relies on shear tests on wallettes, or on standard triplets. Aiming to avoid the behavioural interpretation problems related with the existence of two mortar joints in triplets, this paper investigates the alternative possibility of testing simple couplet specimens. A direct experimental comparison was established with tests on the two specimen configurations (triplets and couplets) performed on two different types of masonry, both characterized by low strength mortars (hydraulic lime and cement based). The obtained results include the evaluation of Mohr-Coulomb parameters, residual shear strengths, second mode fracture energy, and secant shear modulus. The findings point out that couplets yield consistent experimental results and provide systematically higher estimations of all parameters compared to triplets.

The influence of the hygrothermal aging on the strength and stiffness of adhesives used for civil engineering applications with pultruded profiles: an experimental and numerical investigation

ABSTRACT The use of the composite pultruded materials is increasing due to the particular characteristics of lightness, ease of installation, high corrosion resistance and, finally, lower maintenance costs. Even if the bolting technique is the most widely used, especially in the field of civil engineering re-adapting the rules valid for steel structures, thanks to several studies on adhesives, there is reason to believe that the best connection technique for pultruded profiles is gluing (the continuity of the fibers is guaranteed). Current applications involving such materials, strictly related to the field of civil engineering, include bridges, pedestrian and the motorway bridges, roof structures, helipads, solar charging stations, offshore structures, cooling towers and lockgates. In some of these structures, the system (composite material and resin) is in contact with water. Even if there are several studies on the durability of composite pultruded material, current literature referring to adhesives between pultruded adherents needs further investigation. Within this framework, the paper aims to investigate, from an experimental and numerical point of view, the effect of the hygrothermal ageing on both the fracture energy in mode II as well as the strength and stiffness of two commercial epoxy resins taking into account the further effect of the desorption. Finally, in view of a safe design of a bonded joint, limiting its behaviour to the elastic field only, a lower fracture energy value is presented in relation to the classical one.

A Finite Element Method Study of Polymer Exchange Membrane Fuel Cell End Plate Materials by Using Arcan Specimen

In the current days, fuel cells are more preferred to generate electricity due to their positive sides. Because, if they use hydrogen and oxygen as fuel, they only produce electricity, heat, and water. This property of fuel cells is significant because of preventing environmental and chemical pollution so, they contribute to the environment positively. In addition, they have more positive points such as no moving or rotating parts. Therefore, they are no required for mechanical maintenance and not make noise. Besides, they can be used used in a wide range of areas as mobile and stationary power sources for electricity generation. There are many fuel cell types but, proton exchange membrane fuel cell (PEMFC) is more common than the other fuel cell types. It consists of parts such as an endplate, bipolar flow plate, gas diffusion layer, catalyst layer, and membrane. End plates are located on the outer side of PEMFC and hold together its stacks. In the design of the endplates, the state of fracture energy should be considered in the different loading conditions. Because the material may fail if it is designed only by the strength of materials concepts. This paper investigated pure mode I, pure mode II and mixed mode fracture energy behavior of different materials numerically by using Arcan specimen.

Hygrothermal durability of epoxy adhesives used in civil structural applications

Adhesive durability and joint reliability, strictly related to the bonding agents, are key parameters still under evaluation in civil as well as in other engineering fields. Moisture, different environmental agents and temperature (in particular) can strongly affect the performance of the adhesive joints over the time limiting their applicability. The environmental temperature may exceed the glass transition temperature (Tg) of the adhesive formulation entailing relevant changes in its properties, determining, for instance, a transition from a hard to a rubbery behaviour, thus compromising its specific application. Furthermore, due to changes of the temperature values, the structural adhesive can be naturally subjected to a delay or increase in the curing degree. Hence adverse or positive changes in strength and stiffness can be manifested. Within this framework, the topic of the present paper is the study of the hygro-thermal durability of two commercial epoxy resins, suitable for civil engineering applications, respect to the immersion in tap water and sea water for a period of fifteen months at the temperature of 30 °C. To this scope a wide experimental program was developed comprising both End Notch Failure (ENF) tests on the adhesive samples (adherent in glass fiber reinforced polymer, GFRP) for evaluating the pure fracture energy in Mode II of the resins and the water absorption tests for resins and GFRP materials. In general, the results, in terms of fracture energy, show an initial increment (first three-four months) followed by a decrement up to the reaching of a plateau (in the ninth-twelfth month of conditioning). For what concerns the water absorption, the results show that the equilibrium value of both resins is reached in about one month, while that of GFRP samples depend on the type of liquid: three months for tap water and about five months for sea water. Considering the lower activity of the seawater, the longer time to reach the equilibrium value was an expected result.

Mixed mode fracture characterization of brittle and semi-brittle adhesives using the SCB specimen

Fracture mechanics and damage mechanics are widely used to predict the mechanical behavior of adhesive joints. The critical energy release rate is one of the most important parameters in these models. In practice, most adhesive joints experience mixed mode loading conditions. Therefore, mixed mode fracture energy measurement plays an important role in adhesive joint failure analysis. A new test method for mixed mode fracture energy measurement of brittle and semi-brittle adhesive joints is presented in this paper using semi-circular bend specimens. A data reduction scheme based on a finite element analysis is suggested and finite element results are validated by digital image correlation strain measurement technique. The fracture envelops obtained from the proposed specimen are compared to double cantilever beam (DCB), single leg bending (SLB) and, end-notched flexure (ENF) test results. Good agreement between the new specimen and the classic energy measurement methods is observed.

Displacement rate effect in the fracture toughness of glass fiber reinforced polyurethane

Composite structures currently used in the oil industry must meet strict requirements for design and safety reasons. They need to maintain strength under varied displacement rates throughout its lifetime. It is therefore critical to fully understand the fracture behavior of such composites. This work presents experimental results regarding the influence of a range of displacement rates on the fracture energy in mode I, GIc, of glass fiber reinforced polyurethane used in the oil industry to repair and reinforce pipelines with corrosion damage. To determine GIc as a function of displacement rate, double cantilever beam specimens were tested, with displacement rates of 2, 20 and 200 mm/min with different thicknesses. A complementary numerical study was performed with the aim of predicting strength using the measured values. This work has demonstrated a significant influence of the strain rate and composite thickness on GIC of the composite materials, with higher rates and thicker specimens causing an increase in the GIC values.

Dynamic behaviour in mode I fracture toughness of CFRP as a function of temperature

The aim of this work is to assess the influence of high strain rates and testing temperature on the fracture energy in mode I, GIC, of carbon fibre reinforced plastic (CFRP) plates. Double cantilever beam (DCB) specimens were tested to determine GIC as a function of temperature (24 and 80 °C) under an impact load of 4.7 m/s (using a falling-wedge impact test machine), with the results being compared with the values previously determined by the authors under quasi-static loads. This work has demonstrated a significant influence of the testing temperature on the GIC of composite materials, as this value greatly increased for higher temperatures. On the other hand, a less significant influence of the strain rate on GIC was found, which slightly decreased by increasing the strain rate.

Measurement of the fracture energy in mode I of atmospheric ice accreted on different materials using a blister test

Atmospheric ice is formed when supercooled water droplets strike an object such as a tree, aircraft or wind turbine. Its microstructure and properties vary widely according to the flow and thermal conditions prevailing. The present work was conducted in the Cranfield Icing Wind Tunnel for a european project called STORM (efficient ice protection Systems and simulation Techniques Of ice Release on propulsive systeMs). It aimed at collecting data on the fracture energy of atmospheric ice on four different materials - AL2024-T3, Ti-6Al-4V, Platinum and Alexit-411 - using a blister test. This particular test, firstly introduced by Andrews and Lockington (1983), have been adapted by Cranfield University to be able to test the ice adhesion in situ while ice is still accreting on the surface making it closer to real situation. The second part of the paper will focus on the influence of different parameters like the materials ice is accreted on, the total ambient temperature, the tunnel wind speed and the cloud liquid water content which have been investigated over a few icing conditions.

Experimental investigation of an adhesive fracture energy measurement by preventing plastic deformation of substrates in a double cantilever beam test

ABSTRACTA method to prevent substrate damage in a double cantilever beam (DCB) test was experimentally investigated by changing bond-line width. Highly toughened adhesives are developed due to an increase in the demand for structural adhesives. Furthermore, structural materials that are lightweight and excellent in mechanical properties but have limitations in thickness are developed. In contrast, plastic deformation of the substrates is expected when the DCB test is performed with conventional DCB specimens using the aforementioned adhesives and materials. The reduction in the maximum stress on the substrate surface by narrowing a bond-line width is a practical method to prevent plastic deformation when a substrate possesses limited thickness. In this study, the influence of the bond-line width on an adhesive fracture energy in mode I was experimentally investigated by manufacturing DCB specimens in which the bond-line width is narrower than the substrate width. Additionally, the maximum bond-line width to prevent plastic deformation of the substrates was theoretically derived. The evaluated criteria for examining the existence of the plastic deformation by changing the bond-line width exhibited good agreement with the experiment results.

Mode II fracture toughness of CFRP as a function of temperature and strain rate

Abstract Knowledge of the fracture properties of composite materials is fundamental to predict the impact behaviour of the lightweight structures currently used in the automotive industry. Although there is substantial research on mode I fracture behaviour of composites, limited information exists on mode II behaviour. This work aims to fulfil this gap, presenting experimental data regarding the influence of temperature and strain rate on the fracture energy in mode II, G IIC , of composite plates. Significant influence of the strain rate and temperature on G IIC of the composite materials was found. Higher strain rates led to a decrease of G IIC up to 17%. An increase of temperature corresponded to an increase of G IIC up to 15% and a decrease of temperature originated a decrease of G IIC up to 7%.

Mode I fracture toughness of CFRP as a function of temperature and strain rate

Composite structures currently used in the automotive industry must meet strict requirements for safety reasons. They need to maintain strength under varied temperatures and strain rates, including impact. It is therefore critical to fully understand the impact behaviour of composites. This work presents experimental results regarding the influence of a range of temperature and strain rates on the fracture energy in mode I, GIC, of carbon fibre reinforced plastic plates. To determine GICas a function of temperature and strain rate, double cantilever beam specimens were tested at 20, 80 and −30℃, with strain rates of 0.2 and 11 s−1. A complementary numerical study was performed with the aim of predicting strength using the measured values. This work has demonstrated a significant influence of the strain rate and temperature on GICof the composite materials, with higher strain rates and lower temperatures causing a decrease in the GICvalues.

A 3D two-scale multiplane cohesive-zone model for mixed-mode fracture with finite dilation

A 3D multi-scale cohesive-zone model (CZM) combining friction and finite dilation by a multi-plane approach (M-CZM), based on the concept of Representative Multiplane Element (RME), is developed within the mechanics of generalized continua for the analysis of mixed-mode fracture.The proposed M-CZM formulation captures the increase of measured fracture energy in mode II as a natural effect of multi-scale coupling between cohesion, friction and interlocking, employing a reduced set of micromechanical parameters characterized by a well-defined micromechanical interpretation. This permits to devise clear calibration and identification procedures for 3D fracture problems.Upon assessing the retrieval, by a regular 5-plane RME, of a quasi-isotropic response for fracture resistance and for dilation, the M-CZM is employed in FEM simulations of Double-Cantilever Beam (DCB) tests to obtain predictions of mixed mode I–II and mixed mode I–III fracture resistance.The DCB analyses show the key role of the characteristic height of asperities in determining the macroscopic fracture resistance in both mixed mode I–II and I–III interactions. Numerical results also show the independence of the mode-I fracture resistance on the geometry of the beam section and a marked dependence of the measured mixed-mode fracture resistance on the section aspect ratio.

A thermodynamically consistent cohesive-frictional interface model for mixed mode delamination

A new interface constitutive model based on damage mechanics and frictional plasticity is presented. The model is thermodynamically consistent, it is able to accurately reproduce arbitrary mixed mode debonding conditions and it is proved that the separation work is always bounded between the fracture energy in mode I and the fracture energy in mode II. Analytical results are given for proportional loading paths and for two non-proportional loading paths, confirming the correct behavior of the model for complex loading histories. Numerical and analytical solutions are compared for three classical delamination tests and frictional effects on 4ENF are also considered.

Constitutive law of adhesive layer measured with mixed mode bending test

New analytical theory is presented in this paper to measure the mixed mode constitutive law of adhesive bonding. The theory is on the basis of the J-integral theory and the mixed mode bending test. The fracture energy and the mode I/II constitutive law components were obtained at different mode mixity ratios. A comprehensive discussion is carried out with focus on the plastic yielding and initiation of localized damage. In situ SEM was used to analyse the tension/shear deformation mechanisms. The mixed mode fracture energy is found to increase significantly as the mode mixity ratio increased. The tension stress started to decrease after plastic yielding, while the shear stress kept increasing until the emergence of localized damage. This difference was attributed to the anisotropy of the adhesive material, caused by shear banding. The plastic deformation consisted of cavitation caused by tension and shear banding caused by shear. The present method is verified with numerical simulations. The constitutive law measured with the present method can be used to develop new cohesive zone models, and may produce a more accurate analysis of adhesive bonded structures than existing methods do.

A thermodynamically consistent derivation of a frictional-damage cohesive-zone model with different mode I and mode II fracture energies

Abstract The present paper deals with the derivation of an interface model characterized by macroscopic fracture energies which are different in modes I and II, the macroscopic fracture energy being the total energy dissipated per unit of fracture area. It is first shown that thermo-dynamical consistency for a model governed by a single damage variable, combined with the choice of employing an equivalent relative displacement and of a linear softening in the stress-relative displacement law, leads to the coincidence of fracture energies in modes I and II. To retrieve the experimental evidence of a greater fracture energy in mode II, a micro-structured geometry is considered at the typical point of the interface where a Representative Interface Element (RIE) characterized by a periodic arrangement of distinct inclined planes is introduced. The interaction within each of these surfaces is governed by a coupled damage-friction law. A sensitivity analysis of the correlation between micromechanical parameters and the numerically computed single-point microstructural response in mode II is reported. An assessment of the capability of the model in predicting different mixed mode fracture energies is carried out both at the single microstructural interface point level and with a structural example. For the latter a double cantilever beam with uneven bending moments has been analyzed and numerical results are compared with experimental data reported in the literature for different values of mode mixity.